Related papers: A tangential approach to trigonometry

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…

Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the…

An approach to defining quadratic implicit curves is to prescribe two tangent lines and a secant line going through the points of tangency. This paper will show that this method can be generalized to a higher number of tangents, resulting…

In our recent publication we obtained a series expansion of the arctangent function involving complex numbers. In this work we show that this formula can also be expressed as a real rational function.

In this note we study a new cohomology attached to a function along the leaves of complex foliations. We also explain how this cohomology depends on the function and we study a relative cohomology and a Mayer-Vietoris sequence related to…

The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

Let $f$ be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function $T(r,f)$ in terms of the counting function of a homogeneous…

We define the transgression functor which associates to a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle of the manifold.

Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…

This paper studies the integration problem in differential fields that may involve quantities reminiscent of the Weierstrass $\wp$ function, which are defined by a first-order nonlinear differential equation. We extend the classical notion…

We give an elementary characterization of rational functions among meromorphic functions in the complex plane.

We build a tangent structure on the category of divided power algebras using a particular notion of semidirect product. We show that this tangent structure admits an adjoint tangent structure, which involves a version of K\"ahler…

We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouville fractional calculus and demonstrate how the operators may…

Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…

We introduce toric arrangements, essentially finite families of codimension 1 subtori of a torus or of their cosets, as a periodic generalization of hyperplane arrangements, compute cohomology of the complement of such an arrangement and…

We define transalgebraic functions on a compact Riemann surface as meromorphic functions except at a finite number of punctures where they have finite order exponential singularities. This transalgebraic class is a topological…

The celebrated and famous Weierstrass approximation theorem characterizes the set of continuous functions on a compact interval via uniform approximation by algebraic polynomials. This theorem is the first significant result in…

We modify the Whittaker-Watson account of the Eisenstein approach to the trigonometric functions, basing these functions independently on the Eisenstein function $\varepsilon_2$.